Submodular set function

Known as: Submodular, Submodular function 
In mathematics, a submodular set function (also known as a submodular function) is a set function whose value, informally, has the property that the… (More)
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Active learning (machine learning)Alexander SchrijverArtificial intelligenceAutomatic summarization
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Combinatorial optimization

Papers overview

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2015
2015
Rigid Network Design Via Submodular Set Function Optimization
We consider the problem of constructing networks that exhibit desirable algebraic rigidity properties, which can provide… (More)
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Highly Cited
2011
Highly Cited
2011
Maximizing a Monotone Submodular Function Subject to a Matroid Constraint
Let f : 2 → R+ be a monotone submodular set function, and let (X, I) be a matroid. We consider the problem maxS∈I f(S). It is… (More)
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Highly Cited
2011
Highly Cited
2011
A Class of Submodular Functions for Document Summarization
We design a class of submodular functions meant for document summarization tasks. These functions each combine two terms, one… (More)
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Highly Cited
2010
Highly Cited
2010
Multi-document Summarization via Budgeted Maximization of Submodular Functions
We treat the text summarization problem as maximizing a submodular function under a budget constraint. We show, both… (More)
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Highly Cited
2009
Highly Cited
2009
Maximizing submodular set functions subject to multiple linear constraints
The concept of submodularity plays a vital role in combinatorial optimization. In particular, many important optimization… (More)
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Highly Cited
2007
Highly Cited
2007
Revisiting the Greedy Approach to Submodular Set Function Maximization
We consider the problem of maximizing a nondecreasing submodular set function over various constraint structures. Specifically… (More)
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Highly Cited
2007
Highly Cited
2007
Maximizing a Submodular Set Function Subject to a Matroid Constraint (Extended Abstract)
Let f : 2 → R be a non-decreasing submodular set function, and let (N, I) be a matroid. We consider the problem maxS∈I f(S). It… (More)
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Highly Cited
2004
Highly Cited
2004
A note on maximizing a submodular set function subject to a knapsack constraint
In this paper, we obtain an (1 − e−1)-approximation algorithm for maximizing a nondecreasing submodular set function subject to a… (More)
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Highly Cited
2000
Highly Cited
2000
A Combinatorial Algorithm Minimizing Submodular Functions in Strongly Polynomial Time
We give a strongly polynomial-time algorithm minimizing a submodular function f given by a value-giving oracle. The algorithm… (More)
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Highly Cited
1978
Highly Cited
1978
An analysis of approximations for maximizing submodular set functions - I
Let N be a finite set and z be a real-valued function defined on the set of subsets of N that satisfies z(S)+z(T)>-z(SUT)+z(SnT… (More)
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